Final Test: Operating Systems

The grade formula is as follows:

Grade = 0.4 * Theory + 0.6 * Programming

Part 1. Theoretical Questions

Answer the theoretical questions in a few sentences (1-2 paragraphs for a question).

Use your own words. Copy-paste from external sources and other students will result in 100% penalty.

1. Operating system achitecture.
   • List the main components of an operating system.
   • List the tasks a typical operating system solves.
   • What is a system call?
2. Processes and threads.
   • Give definitions of process and thread.
   • What is the difference between them?
   • What inter-process communication mechanisms do you know?
   • What synchronization mechanisms do you now?
3. Permissions.
   • What Linux files types to you know?
   • What access rights and permission groups do you know?
   • Study the output of the ls -li command below.

   • What can you say about file1, file2, and file3?

     acos@acos-vm:~/folder$ ls -li
     total 44
     268508 -rwsr-xr-x 2 myuser acos 16832 июн 17 14:04 file1
     262605 drwxr-xr-- 2 acos   acos  4096 июн 17 14:08 file2
     268508 -rwsr-xr-x 2 myuser acos 16832 июн 17 14:04 file3
     

Part 2. Programming Task

Write a program in C that does the following:

• Calculates the value of the specified function in the range from argv[1] to argv[2] with step argv[3].
• Writes pairs <function argument>, <function result>) into text file output.csv (CSV format).
• The function to be calculated has the following format:

  f(x) = f0(f1(x), f2(x), f3(x), f4(x))
  

  , where:

  • x is the function argument;
  • f0-f4 are functions that are individual according to the variant.

Requirements:

• Grade 4: make all calculations in a single process;
• Grade 8: execute the f0 function for the entire value range in a child process and return the resulting values to the parent process using IPC (a pipe or other type of IPC you like);
• Grade 10: execute f0 in the parent process and f1-f4 in separate child processes. Return the calculated values of f1-f4 to f0 using IPC (a pipe or other type of IPC you like).

Hints

• Functions f1-f4 have the following structure:

  double f1(double x) {
      return <math expr>;
  }
  

• Command-line arguments (strings) can be converted to double using the atof function.
• Mathematical functions (such as sin, cos, pow, exp etc.) and constants (M_E) are provided in the math.h library.
• Programs using library <math.h> must be linked with the m library: use the -lm GCC flag.
• Use the fopen, fprintf, and fclose functions to write data to the file.
• Multi-process calculations:
  • Child: a function is calculated for a range of values and results are written to IPC;
  • Parent: values are read from IPC in a loop and printed or used in other calculations.

Variants

Choose your variant number according to your number in the list of students.

Note: the ^ symbol means “power”.

---

Group 191

1. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 7*x^3 + 5*x^2 + 3*x + 2
    f2(x) = sin(2*x)*3 + 2
    f3(x) = 3^x + 5
    f4(x) = 1 / (1 + e^(-2*x))
   

2. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 6*x^3 + 9*x^2 + 3*x + 6
    f2(x) = sin(9*x)*4 + 7
    f3(x) = 2^x + 5
    f4(x) = 1 / (1 + e^(-7*x))
   

3. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 2*x^3 + 6*x^2 + 6*x + 9
    f2(x) = sin(3*x)*7 + 3
    f3(x) = 7^x + 9
    f4(x) = 1 / (1 + e^(-7*x))
   

4. Variant

    f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
    f1(x) = 6*x^3 + 2*x^2 + 9*x + 3
    f2(x) = sin(2*x)*4 + 6
    f3(x) = 5^x + 8
    f4(x) = 1 / (1 + e^(-4*x))
   

5. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 4*x^3 + 8*x^2 + 5*x + 2
    f2(x) = sin(4*x)*5 + 6
    f3(x) = 9^x + 7
    f4(x) = 1 / (1 + e^(-8*x))
   

6. Variant

    f0(a, b, c, d) = MAX(a, b, c, d)
    f1(x) = 3*x^3 + 7*x^2 + 2*x + 5
    f2(x) = sin(9*x)*4 + 9
    f3(x) = 4^x + 3
    f4(x) = 1 / (1 + e^(-6*x))
   

7. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 5*x^3 + 5*x^2 + 7*x + 6
    f2(x) = sin(3*x)*8 + 2
    f3(x) = 8^x + 5
    f4(x) = 1 / (1 + e^(-8*x))
   

8. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 7*x^3 + 8*x^2 + 5*x + 4
    f2(x) = sin(5*x)*4 + 2
    f3(x) = 7^x + 9
    f4(x) = 1 / (1 + e^(-8*x))
   

9. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 7*x^3 + 7*x^2 + 7*x + 3
    f2(x) = sin(2*x)*6 + 8
    f3(x) = 3^x + 3
    f4(x) = 1 / (1 + e^(-2*x))
   

10. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 5*x^3 + 4*x^2 + 7*x + 2
     f2(x) = sin(6*x)*9 + 5
     f3(x) = 4^x + 2
     f4(x) = 1 / (1 + e^(-4*x))
    

11. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 5*x^3 + 9*x^2 + 3*x + 2
     f2(x) = sin(6*x)*2 + 8
     f3(x) = 7^x + 3
     f4(x) = 1 / (1 + e^(-4*x))
    

12. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 5*x^3 + 8*x^2 + 2*x + 7
     f2(x) = sin(4*x)*5 + 5
     f3(x) = 8^x + 6
     f4(x) = 1 / (1 + e^(-5*x))
    

13. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 6*x^3 + 2*x^2 + 7*x + 6
     f2(x) = sin(3*x)*3 + 2
     f3(x) = 6^x + 2
     f4(x) = 1 / (1 + e^(-7*x))
    

14. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 9*x^3 + 6*x^2 + 3*x + 5
     f2(x) = sin(8*x)*7 + 8
     f3(x) = 5^x + 2
     f4(x) = 1 / (1 + e^(-6*x))
    

15. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 3*x^3 + 2*x^2 + 7*x + 2
     f2(x) = sin(6*x)*7 + 2
     f3(x) = 2^x + 9
     f4(x) = 1 / (1 + e^(-3*x))
    

16. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 6*x^3 + 9*x^2 + 2*x + 9
     f2(x) = sin(5*x)*3 + 4
     f3(x) = 9^x + 7
     f4(x) = 1 / (1 + e^(-6*x))
    

17. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 2*x^3 + 2*x^2 + 7*x + 9
     f2(x) = sin(7*x)*3 + 7
     f3(x) = 7^x + 3
     f4(x) = 1 / (1 + e^(-5*x))
    

18. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 5*x^3 + 2*x^2 + 7*x + 2
     f2(x) = sin(5*x)*8 + 5
     f3(x) = 6^x + 7
     f4(x) = 1 / (1 + e^(-9*x))
    

19. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 9*x^3 + 6*x^2 + 8*x + 3
     f2(x) = sin(8*x)*5 + 7
     f3(x) = 4^x + 8
     f4(x) = 1 / (1 + e^(-8*x))
    

20. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 3*x^3 + 3*x^2 + 4*x + 7
     f2(x) = sin(3*x)*7 + 5
     f3(x) = 6^x + 4
     f4(x) = 1 / (1 + e^(-3*x))
    

21. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 5*x^3 + 8*x^2 + 7*x + 2
     f2(x) = sin(9*x)*9 + 7
     f3(x) = 4^x + 5
     f4(x) = 1 / (1 + e^(-9*x))
    

22. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 9*x^3 + 9*x^2 + 2*x + 3
     f2(x) = sin(7*x)*8 + 6
     f3(x) = 2^x + 6
     f4(x) = 1 / (1 + e^(-6*x))
    

23. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 3*x^3 + 5*x^2 + 4*x + 3
     f2(x) = sin(5*x)*3 + 8
     f3(x) = 2^x + 4
     f4(x) = 1 / (1 + e^(-4*x))
    

24. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 4*x^3 + 6*x^2 + 3*x + 5
     f2(x) = sin(9*x)*3 + 4
     f3(x) = 2^x + 3
     f4(x) = 1 / (1 + e^(-2*x))
    

25. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 3*x^3 + 5*x^2 + 3*x + 5
     f2(x) = sin(4*x)*5 + 5
     f3(x) = 4^x + 6
     f4(x) = 1 / (1 + e^(-3*x))
    

26. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 3*x^3 + 9*x^2 + 2*x + 5
     f2(x) = sin(4*x)*7 + 4
     f3(x) = 9^x + 4
     f4(x) = 1 / (1 + e^(-2*x))
    

---

Group 192

1. Variant

    f0(a, b, c, d) = MAX(a, b, c, d)
    f1(x) = 7*x^3 + 9*x^2 + 8*x + 2
    f2(x) = sin(4*x)*5 + 3
    f3(x) = 4^x + 2
    f4(x) = 1 / (1 + e^(-2*x))
   

2. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 8*x^3 + 8*x^2 + 5*x + 3
    f2(x) = sin(3*x)*2 + 8
    f3(x) = 6^x + 2
    f4(x) = 1 / (1 + e^(-9*x))
   

3. Variant

    f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
    f1(x) = 3*x^3 + 5*x^2 + 2*x + 5
    f2(x) = sin(9*x)*4 + 8
    f3(x) = 5^x + 7
    f4(x) = 1 / (1 + e^(-3*x))
   

4. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 2*x^3 + 3*x^2 + 5*x + 8
    f2(x) = sin(5*x)*9 + 2
    f3(x) = 5^x + 4
    f4(x) = 1 / (1 + e^(-4*x))
   

5. Variant

    f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
    f1(x) = 2*x^3 + 9*x^2 + 7*x + 2
    f2(x) = sin(7*x)*4 + 4
    f3(x) = 8^x + 9
    f4(x) = 1 / (1 + e^(-8*x))
   

6. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 9*x^3 + 5*x^2 + 2*x + 6
    f2(x) = sin(9*x)*4 + 7
    f3(x) = 5^x + 2
    f4(x) = 1 / (1 + e^(-6*x))
   

7. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 9*x^3 + 7*x^2 + 5*x + 7
    f2(x) = sin(5*x)*9 + 7
    f3(x) = 6^x + 2
    f4(x) = 1 / (1 + e^(-6*x))
   

8. Variant

    f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
    f1(x) = 7*x^3 + 9*x^2 + 6*x + 3
    f2(x) = sin(6*x)*5 + 7
    f3(x) = 8^x + 3
    f4(x) = 1 / (1 + e^(-4*x))
   

9. Variant

    f0(a, b, c, d) = MAX(a, b, c, d)
    f1(x) = 4*x^3 + 8*x^2 + 8*x + 5
    f2(x) = sin(3*x)*5 + 9
    f3(x) = 9^x + 8
    f4(x) = 1 / (1 + e^(-3*x))
   

10. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 8*x^3 + 6*x^2 + 6*x + 8
     f2(x) = sin(8*x)*2 + 2
     f3(x) = 8^x + 3
     f4(x) = 1 / (1 + e^(-6*x))
    

11. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 7*x^3 + 7*x^2 + 5*x + 5
     f2(x) = sin(7*x)*6 + 5
     f3(x) = 8^x + 5
     f4(x) = 1 / (1 + e^(-3*x))
    

12. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 7*x^3 + 8*x^2 + 8*x + 2
     f2(x) = sin(5*x)*4 + 3
     f3(x) = 9^x + 2
     f4(x) = 1 / (1 + e^(-9*x))
    

13. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 4*x^3 + 3*x^2 + 3*x + 5
     f2(x) = sin(4*x)*3 + 5
     f3(x) = 7^x + 7
     f4(x) = 1 / (1 + e^(-7*x))
    

14. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 2*x^3 + 2*x^2 + 8*x + 5
     f2(x) = sin(3*x)*6 + 4
     f3(x) = 5^x + 3
     f4(x) = 1 / (1 + e^(-4*x))
    

15. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 7*x^3 + 2*x^2 + 3*x + 2
     f2(x) = sin(2*x)*2 + 9
     f3(x) = 6^x + 5
     f4(x) = 1 / (1 + e^(-3*x))
    

16. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 4*x^3 + 4*x^2 + 9*x + 8
     f2(x) = sin(4*x)*7 + 3
     f3(x) = 2^x + 7
     f4(x) = 1 / (1 + e^(-8*x))
    

17. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 5*x^3 + 4*x^2 + 4*x + 8
     f2(x) = sin(8*x)*2 + 8
     f3(x) = 5^x + 9
     f4(x) = 1 / (1 + e^(-9*x))
    

18. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 5*x^3 + 4*x^2 + 8*x + 7
     f2(x) = sin(6*x)*6 + 5
     f3(x) = 8^x + 4
     f4(x) = 1 / (1 + e^(-5*x))
    

19. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 8*x^3 + 3*x^2 + 7*x + 6
     f2(x) = sin(9*x)*8 + 2
     f3(x) = 7^x + 5
     f4(x) = 1 / (1 + e^(-5*x))
    

20. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 4*x^3 + 5*x^2 + 4*x + 6
     f2(x) = sin(9*x)*6 + 6
     f3(x) = 5^x + 5
     f4(x) = 1 / (1 + e^(-6*x))
    

21. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 2*x^3 + 7*x^2 + 3*x + 8
     f2(x) = sin(8*x)*7 + 9
     f3(x) = 6^x + 6
     f4(x) = 1 / (1 + e^(-9*x))
    

22. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 2*x^3 + 2*x^2 + 2*x + 7
     f2(x) = sin(9*x)*5 + 5
     f3(x) = 7^x + 6
     f4(x) = 1 / (1 + e^(-3*x))
    

23. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 4*x^3 + 8*x^2 + 8*x + 6
     f2(x) = sin(7*x)*4 + 5
     f3(x) = 7^x + 4
     f4(x) = 1 / (1 + e^(-7*x))
    

24. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 4*x^3 + 4*x^2 + 4*x + 9
     f2(x) = sin(5*x)*4 + 7
     f3(x) = 8^x + 6
     f4(x) = 1 / (1 + e^(-4*x))
    

25. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 9*x^3 + 5*x^2 + 9*x + 5
     f2(x) = sin(8*x)*9 + 9
     f3(x) = 4^x + 3
     f4(x) = 1 / (1 + e^(-6*x))
    

26. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 3*x^3 + 9*x^2 + 8*x + 9
     f2(x) = sin(6*x)*7 + 3
     f3(x) = 2^x + 6
     f4(x) = 1 / (1 + e^(-2*x))
    

27. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 8*x^3 + 9*x^2 + 9*x + 8
     f2(x) = sin(9*x)*8 + 2
     f3(x) = 8^x + 2
     f4(x) = 1 / (1 + e^(-6*x))
    

---

Group 193

1. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 2*x^3 + 9*x^2 + 9*x + 3
    f2(x) = sin(2*x)*5 + 7
    f3(x) = 2^x + 7
    f4(x) = 1 / (1 + e^(-8*x))
   

2. Variant

    f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
    f1(x) = 3*x^3 + 2*x^2 + 4*x + 9
    f2(x) = sin(3*x)*7 + 2
    f3(x) = 4^x + 6
    f4(x) = 1 / (1 + e^(-4*x))
   

3. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 8*x^3 + 6*x^2 + 6*x + 6
    f2(x) = sin(5*x)*2 + 7
    f3(x) = 6^x + 6
    f4(x) = 1 / (1 + e^(-4*x))
   

4. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 4*x^3 + 9*x^2 + 3*x + 6
    f2(x) = sin(5*x)*6 + 9
    f3(x) = 3^x + 6
    f4(x) = 1 / (1 + e^(-5*x))
   

5. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 8*x^3 + 2*x^2 + 4*x + 3
    f2(x) = sin(3*x)*9 + 3
    f3(x) = 9^x + 8
    f4(x) = 1 / (1 + e^(-7*x))
   

6. Variant

    f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
    f1(x) = 9*x^3 + 2*x^2 + 8*x + 7
    f2(x) = sin(5*x)*2 + 6
    f3(x) = 5^x + 2
    f4(x) = 1 / (1 + e^(-3*x))
   

7. Variant

    f0(a, b, c, d) = MAX(a, b, c, d)
    f1(x) = 4*x^3 + 6*x^2 + 4*x + 8
    f2(x) = sin(6*x)*2 + 2
    f3(x) = 2^x + 4
    f4(x) = 1 / (1 + e^(-3*x))
   

8. Variant

    f0(a, b, c, d) = MAX(a, b, c, d)
    f1(x) = 2*x^3 + 7*x^2 + 5*x + 6
    f2(x) = sin(3*x)*7 + 6
    f3(x) = 8^x + 3
    f4(x) = 1 / (1 + e^(-3*x))
   

9. Variant

    f0(a, b, c, d) = MIN(a, b, c, d)
    f1(x) = 5*x^3 + 4*x^2 + 5*x + 8
    f2(x) = sin(6*x)*5 + 9
    f3(x) = 6^x + 4
    f4(x) = 1 / (1 + e^(-4*x))
   

10. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 5*x^3 + 7*x^2 + 9*x + 4
     f2(x) = sin(2*x)*7 + 9
     f3(x) = 9^x + 5
     f4(x) = 1 / (1 + e^(-7*x))
    

11. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 5*x^3 + 7*x^2 + 8*x + 5
     f2(x) = sin(5*x)*2 + 8
     f3(x) = 8^x + 3
     f4(x) = 1 / (1 + e^(-3*x))
    

12. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 3*x^3 + 9*x^2 + 2*x + 8
     f2(x) = sin(9*x)*8 + 9
     f3(x) = 2^x + 4
     f4(x) = 1 / (1 + e^(-9*x))
    

13. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 2*x^3 + 2*x^2 + 8*x + 9
     f2(x) = sin(7*x)*6 + 9
     f3(x) = 3^x + 4
     f4(x) = 1 / (1 + e^(-3*x))
    

14. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 6*x^3 + 9*x^2 + 6*x + 4
     f2(x) = sin(6*x)*6 + 9
     f3(x) = 3^x + 4
     f4(x) = 1 / (1 + e^(-2*x))
    

15. Variant

     f0(a, b, c, d) = AVG(a, b, c, d) = (a + b + c + d) / 4
     f1(x) = 9*x^3 + 5*x^2 + 6*x + 2
     f2(x) = sin(9*x)*8 + 9
     f3(x) = 4^x + 3
     f4(x) = 1 / (1 + e^(-7*x))
    

16. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 7*x^3 + 6*x^2 + 8*x + 5
     f2(x) = sin(9*x)*2 + 7
     f3(x) = 7^x + 9
     f4(x) = 1 / (1 + e^(-9*x))
    

17. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 5*x^3 + 6*x^2 + 5*x + 5
     f2(x) = sin(2*x)*3 + 6
     f3(x) = 2^x + 7
     f4(x) = 1 / (1 + e^(-3*x))
    

18. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 5*x^3 + 4*x^2 + 3*x + 2
     f2(x) = sin(4*x)*9 + 6
     f3(x) = 7^x + 6
     f4(x) = 1 / (1 + e^(-8*x))
    

19. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 5*x^3 + 6*x^2 + 9*x + 9
     f2(x) = sin(3*x)*2 + 7
     f3(x) = 7^x + 3
     f4(x) = 1 / (1 + e^(-7*x))
    

20. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 5*x^3 + 9*x^2 + 4*x + 7
     f2(x) = sin(2*x)*7 + 8
     f3(x) = 5^x + 7
     f4(x) = 1 / (1 + e^(-5*x))
    

21. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 8*x^3 + 9*x^2 + 6*x + 3
     f2(x) = sin(8*x)*3 + 5
     f3(x) = 5^x + 9
     f4(x) = 1 / (1 + e^(-7*x))
    

22. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 2*x^3 + 2*x^2 + 4*x + 5
     f2(x) = sin(8*x)*9 + 8
     f3(x) = 2^x + 3
     f4(x) = 1 / (1 + e^(-8*x))
    

23. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 3*x^3 + 4*x^2 + 3*x + 6
     f2(x) = sin(2*x)*7 + 8
     f3(x) = 8^x + 6
     f4(x) = 1 / (1 + e^(-5*x))
    

24. Variant

     f0(a, b, c, d) = MAX(a, b, c, d)
     f1(x) = 5*x^3 + 8*x^2 + 2*x + 2
     f2(x) = sin(6*x)*5 + 4
     f3(x) = 6^x + 8
     f4(x) = 1 / (1 + e^(-5*x))
    

25. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 8*x^3 + 8*x^2 + 6*x + 9
     f2(x) = sin(5*x)*7 + 7
     f3(x) = 6^x + 3
     f4(x) = 1 / (1 + e^(-2*x))
    

26. Variant

     f0(a, b, c, d) = MIN(a, b, c, d)
     f1(x) = 8*x^3 + 6*x^2 + 5*x + 4
     f2(x) = sin(2*x)*5 + 5
     f3(x) = 5^x + 2
     f4(x) = 1 / (1 + e^(-9*x))
    

27. Variant

     f0(a, b, c, d) = L2(a, b, c, d) = sqrt(a^2 + b^2 + c^2 + d^2)
     f1(x) = 5*x^3 + 3*x^2 + 5*x + 7
     f2(x) = sin(5*x)*4 + 4
     f3(x) = 8^x + 2
     f4(x) = 1 / (1 + e^(-9*x))